mirror of
https://gitlab.com/sheaf/metabrush.git
synced 2024-11-05 14:53:37 +00:00
Restructure project & update bounds
This commit is contained in:
parent
1368825103
commit
6b658acedd
115
MetaBrush.cabal
115
MetaBrush.cabal
|
@ -29,34 +29,27 @@ flag asserts
|
|||
default: False
|
||||
manual: True
|
||||
|
||||
flag use-fma
|
||||
description: Use fused-muliply add instructions to implement interval arithmetic.
|
||||
default: False
|
||||
manual: True
|
||||
|
||||
common common
|
||||
|
||||
build-depends:
|
||||
base
|
||||
>= 4.17 && < 4.19
|
||||
brush-strokes
|
||||
^>= 0.1.0.0
|
||||
, base
|
||||
>= 4.17 && < 5
|
||||
, acts
|
||||
^>= 0.3.1.0
|
||||
, code-page
|
||||
^>= 0.2.1
|
||||
, containers
|
||||
>= 0.6.0.1 && < 0.7
|
||||
>= 0.6.0.1 && < 0.8
|
||||
, deepseq
|
||||
>= 1.4.4.0 && < 1.5
|
||||
>= 1.4.4.0 && < 1.6
|
||||
, generic-lens
|
||||
>= 2.2 && < 2.3
|
||||
, groups
|
||||
^>= 0.5.3
|
||||
, groups-generic
|
||||
^>= 0.3.1.0
|
||||
, primitive
|
||||
^>= 0.7.1.0
|
||||
, rounded-hw
|
||||
^>= 0.3
|
||||
^>= 0.9.0.0
|
||||
, transformers
|
||||
>= 0.5.6.2 && < 0.7
|
||||
|
||||
|
@ -94,14 +87,11 @@ common common
|
|||
UnboxedTuples
|
||||
ViewPatterns
|
||||
|
||||
if impl(ghc >= 9.8)
|
||||
default-extensions:
|
||||
TypeAbstractions
|
||||
|
||||
ghc-options:
|
||||
-O2
|
||||
-fexpose-all-unfoldings
|
||||
-- -funfolding-use-threshold=1000
|
||||
-fspecialise-aggressively
|
||||
-flate-dmd-anal
|
||||
-fmax-worker-args=200
|
||||
-optc-O3
|
||||
-Wall
|
||||
-Wcompat
|
||||
-fwarn-missing-local-signatures
|
||||
|
@ -114,14 +104,6 @@ common common
|
|||
cpp-options:
|
||||
-DASSERTS
|
||||
|
||||
if flag(use-fma)
|
||||
cpp-options:
|
||||
-DUSE_FMA
|
||||
ghc-options:
|
||||
-mfma
|
||||
if impl(ghc < 9.7)
|
||||
buildable: False
|
||||
|
||||
autogen-modules:
|
||||
Paths_MetaBrush
|
||||
|
||||
|
@ -131,11 +113,10 @@ common common
|
|||
common extras
|
||||
|
||||
build-depends:
|
||||
|
||||
directory
|
||||
>= 1.3.4.0 && < 1.4
|
||||
, filepath
|
||||
^>= 1.4.2.1
|
||||
>= 1.4.2.1 && < 1.6
|
||||
, hashable
|
||||
>= 1.3.0.0 && < 1.5
|
||||
, lens
|
||||
|
@ -147,9 +128,9 @@ common extras
|
|||
, stm
|
||||
^>= 2.5.0.0
|
||||
, text
|
||||
>= 1.2.3.1 && < 2.1
|
||||
^>= 2.1.1
|
||||
, unordered-containers
|
||||
>= 0.2.11 && < 0.2.20
|
||||
>= 0.2.11 && < 0.3
|
||||
, waargonaut
|
||||
^>= 0.8.0.2
|
||||
|
||||
|
@ -175,64 +156,6 @@ common gtk
|
|||
, haskell-gi-base
|
||||
>= 0.26 && < 0.27
|
||||
|
||||
|
||||
library splines
|
||||
|
||||
import:
|
||||
common
|
||||
|
||||
hs-source-dirs:
|
||||
src/splines
|
||||
|
||||
default-language:
|
||||
Haskell2010
|
||||
|
||||
exposed-modules:
|
||||
Math.Algebra.Dual
|
||||
, Math.Bezier.Cubic
|
||||
, Math.Bezier.Cubic.Fit
|
||||
, Math.Bezier.Quadratic
|
||||
, Math.Bezier.Spline
|
||||
, Math.Bezier.Stroke
|
||||
, Math.Bezier.Stroke.EnvelopeEquation
|
||||
, Math.Differentiable
|
||||
, Math.Epsilon
|
||||
, Math.Interval
|
||||
, Math.Linear
|
||||
, Math.Linear.Solve
|
||||
, Math.Module
|
||||
, Math.Monomial
|
||||
, Math.Orientation
|
||||
, Math.Ring
|
||||
, Math.Roots
|
||||
, Debug.Utils
|
||||
|
||||
other-modules:
|
||||
Math.Algebra.Dual.Internal
|
||||
, Math.Interval.Internal
|
||||
, Math.Linear.Internal
|
||||
, Math.Module.Internal
|
||||
, TH.Utils
|
||||
|
||||
if flag(use-fma)
|
||||
other-modules:
|
||||
Math.Interval.FMA
|
||||
|
||||
build-depends:
|
||||
bifunctors
|
||||
>= 5.5.4 && < 5.6
|
||||
, eigen
|
||||
^>= 3.3.7.0
|
||||
, parallel
|
||||
^>= 3.2.2.0
|
||||
, prim-instances
|
||||
^>= 0.2
|
||||
, vector
|
||||
>= 0.12.1.2 && < 0.14
|
||||
, template-haskell
|
||||
>= 2.18 && < 2.20
|
||||
|
||||
|
||||
library metabrushes
|
||||
|
||||
import:
|
||||
|
@ -259,8 +182,7 @@ library metabrushes
|
|||
, MetaBrush.Util
|
||||
|
||||
build-depends:
|
||||
splines
|
||||
, atomic-file-ops
|
||||
atomic-file-ops
|
||||
^>= 0.3.0.0
|
||||
, bytestring
|
||||
>= 0.10.10.0 && < 0.12
|
||||
|
@ -282,9 +204,6 @@ executable cusps
|
|||
other-modules:
|
||||
Math.Interval.Abstract
|
||||
|
||||
build-depends:
|
||||
splines
|
||||
|
||||
|
||||
executable convert-metafont
|
||||
|
||||
|
@ -304,7 +223,6 @@ executable convert-metafont
|
|||
MetaBrush.MetaFont.Convert
|
||||
|
||||
build-depends:
|
||||
splines,
|
||||
metabrushes,
|
||||
diagrams-contrib,
|
||||
diagrams-lib,
|
||||
|
@ -358,7 +276,6 @@ executable MetaBrush
|
|||
-threaded -rtsopts
|
||||
|
||||
build-depends:
|
||||
splines
|
||||
, metabrushes
|
||||
metabrushes
|
||||
, tardis
|
||||
>= 0.4.2.0 && < 0.5
|
||||
|
|
152
brush-strokes/brush-strokes.cabal
Normal file
152
brush-strokes/brush-strokes.cabal
Normal file
|
@ -0,0 +1,152 @@
|
|||
cabal-version: 3.0
|
||||
name: brush-strokes
|
||||
version: 0.1.0.0
|
||||
synopsis: Stroking brush paths
|
||||
category: Calligraphy, Geometry, Graphics
|
||||
license: BSD-3-Clause
|
||||
homepage: https://gitlab.com/sheaf/MetaBrush
|
||||
build-type: Simple
|
||||
description:
|
||||
Computing brush strokes using Bézier curves.
|
||||
|
||||
flag use-fma
|
||||
description: Use fused-muliply add instructions to implement interval arithmetic.
|
||||
default: True
|
||||
manual: True
|
||||
|
||||
common common
|
||||
|
||||
build-depends:
|
||||
base
|
||||
>= 4.17 && < 4.20
|
||||
, acts
|
||||
^>= 0.3.1.0
|
||||
, code-page
|
||||
^>= 0.2.1
|
||||
, containers
|
||||
>= 0.6.0.1 && < 0.8
|
||||
, deepseq
|
||||
>= 1.4.4.0 && < 1.6
|
||||
, generic-lens
|
||||
>= 2.2 && < 2.3
|
||||
, groups
|
||||
^>= 0.5.3
|
||||
, groups-generic
|
||||
^>= 0.3.1.0
|
||||
, primitive
|
||||
^>= 0.9.0.0
|
||||
, rounded-hw
|
||||
^>= 0.4
|
||||
, transformers
|
||||
>= 0.5.6.2 && < 0.7
|
||||
|
||||
default-extensions:
|
||||
BangPatterns
|
||||
BlockArguments
|
||||
ConstraintKinds
|
||||
DataKinds
|
||||
DeriveAnyClass
|
||||
DeriveTraversable
|
||||
DeriveGeneric
|
||||
DerivingVia
|
||||
FlexibleContexts
|
||||
FlexibleInstances
|
||||
FunctionalDependencies
|
||||
GADTs
|
||||
GeneralisedNewtypeDeriving
|
||||
InstanceSigs
|
||||
LambdaCase
|
||||
LexicalNegation
|
||||
MagicHash
|
||||
MultiWayIf
|
||||
NamedFieldPuns
|
||||
NoStarIsType
|
||||
PatternSynonyms
|
||||
RankNTypes
|
||||
RecordWildCards
|
||||
RoleAnnotations
|
||||
StandaloneDeriving
|
||||
StandaloneKindSignatures
|
||||
TupleSections
|
||||
TypeApplications
|
||||
TypeFamilies
|
||||
TypeOperators
|
||||
UnboxedTuples
|
||||
ViewPatterns
|
||||
|
||||
ghc-options:
|
||||
-O2
|
||||
-fexpose-all-unfoldings
|
||||
-- -funfolding-use-threshold=1000
|
||||
-fspecialise-aggressively
|
||||
-flate-dmd-anal
|
||||
-fmax-worker-args=200
|
||||
-optc-O3
|
||||
-Wall
|
||||
-Wcompat
|
||||
-fwarn-missing-local-signatures
|
||||
-fwarn-incomplete-patterns
|
||||
-fwarn-incomplete-uni-patterns
|
||||
-fwarn-missing-deriving-strategies
|
||||
-fno-warn-unticked-promoted-constructors
|
||||
|
||||
if flag(use-fma)
|
||||
cpp-options:
|
||||
-DUSE_FMA
|
||||
ghc-options:
|
||||
-mfma
|
||||
build-depends:
|
||||
base
|
||||
>= 4.19
|
||||
|
||||
library
|
||||
|
||||
import:
|
||||
common
|
||||
|
||||
hs-source-dirs:
|
||||
src
|
||||
|
||||
default-language:
|
||||
Haskell2010
|
||||
|
||||
exposed-modules:
|
||||
Math.Algebra.Dual
|
||||
, Math.Bezier.Cubic
|
||||
, Math.Bezier.Cubic.Fit
|
||||
, Math.Bezier.Quadratic
|
||||
, Math.Bezier.Spline
|
||||
, Math.Bezier.Stroke
|
||||
, Math.Bezier.Stroke.EnvelopeEquation
|
||||
, Math.Differentiable
|
||||
, Math.Epsilon
|
||||
, Math.Interval
|
||||
, Math.Linear
|
||||
, Math.Linear.Solve
|
||||
, Math.Module
|
||||
, Math.Monomial
|
||||
, Math.Orientation
|
||||
, Math.Ring
|
||||
, Math.Roots
|
||||
, Debug.Utils
|
||||
|
||||
other-modules:
|
||||
Math.Algebra.Dual.Internal
|
||||
, Math.Interval.Internal
|
||||
, Math.Linear.Internal
|
||||
, Math.Module.Internal
|
||||
, TH.Utils
|
||||
|
||||
if flag(use-fma)
|
||||
other-modules:
|
||||
Math.Interval.FMA
|
||||
|
||||
build-depends:
|
||||
bifunctors
|
||||
>= 5.5.4 && < 5.7
|
||||
, eigen
|
||||
^>= 3.3.7.0
|
||||
, parallel
|
||||
^>= 3.2.2.0
|
||||
, template-haskell
|
||||
>= 2.18 && < 2.22
|
28
brush-strokes/cabal.project
Normal file
28
brush-strokes/cabal.project
Normal file
|
@ -0,0 +1,28 @@
|
|||
packages: .
|
||||
|
||||
constraints:
|
||||
acts -finitary,
|
||||
rounded-hw -pure-hs -c99 -avx512 +ghc-prim -x87-long-double
|
||||
|
||||
allow-newer:
|
||||
acts:base, acts:deepseq,
|
||||
groups-generic:base,
|
||||
eigen:primitive,
|
||||
|
||||
-------------
|
||||
-- GHC 9.4 --
|
||||
-------------
|
||||
|
||||
-- eigen
|
||||
source-repository-package
|
||||
type: git
|
||||
location: https://github.com/chessai/eigen
|
||||
tag: 1790fdf9138970dde0dbabf8b270698145a4a88c
|
||||
|
||||
-------------
|
||||
-- GHC 9.6 --
|
||||
-------------
|
||||
|
||||
-------------
|
||||
-- GHC 9.8 --
|
||||
-------------
|
|
@ -1,6 +1,5 @@
|
|||
module Debug.Utils ( trace ) where
|
||||
|
||||
|
||||
-- base
|
||||
import System.IO
|
||||
( BufferMode(..), hSetBuffering, hFlush, hPutStrLn, stdout )
|
|
@ -6,9 +6,6 @@
|
|||
|
||||
{-# OPTIONS_GHC -Wno-orphans -O2 #-}
|
||||
|
||||
{-# OPTIONS_GHC -ddump-splices -ddump-simpl -ddump-cmm -ddump-to-file -dno-typeable-binds
|
||||
-dsuppress-unfoldings -dsuppress-coercions #-}
|
||||
|
||||
module Math.Algebra.Dual
|
||||
( C(..), D
|
||||
, HasChainRule(..), chainRule
|
|
@ -46,7 +46,12 @@ import qualified Control.Parallel.Strategies as Parallel.Strategy
|
|||
|
||||
-- primitive
|
||||
import Data.Primitive.PrimArray
|
||||
( primArrayFromListN, unsafeThawPrimArray )
|
||||
( MutablePrimArray
|
||||
, generatePrimArray
|
||||
, primArrayFromListN
|
||||
, unsafeThawPrimArray
|
||||
, readPrimArray, writePrimArray
|
||||
)
|
||||
|
||||
-- transformers
|
||||
import Control.Monad.Trans.State.Strict
|
||||
|
@ -54,14 +59,6 @@ import Control.Monad.Trans.State.Strict
|
|||
import Control.Monad.Trans.Class
|
||||
( lift )
|
||||
|
||||
-- vector
|
||||
import qualified Data.Vector.Unboxed.Mutable as Unboxed
|
||||
( MVector )
|
||||
import qualified Data.Vector.Unboxed.Mutable as Unboxed.MVector
|
||||
( unsafeRead, unsafeWrite )
|
||||
import qualified Data.Vector.Unboxed as Unboxed.Vector
|
||||
( unsafeThaw, generate )
|
||||
|
||||
-- MetaBrush
|
||||
import qualified Math.Bezier.Cubic as Cubic
|
||||
( Bezier(..), bezier, ddist )
|
||||
|
@ -202,7 +199,7 @@ fitPiece
|
|||
fitPiece dist_tol t_tol maxIters p tp qs r tr =
|
||||
runST do
|
||||
-- Initialise the parameter values to a uniform subdivision.
|
||||
ts <- Unboxed.Vector.unsafeThaw ( Unboxed.Vector.generate n uniform )
|
||||
ts <- unsafeThawPrimArray $ generatePrimArray n uniform
|
||||
loop ts 0
|
||||
where
|
||||
n :: Int
|
||||
|
@ -216,12 +213,12 @@ fitPiece dist_tol t_tol maxIters p tp qs r tr =
|
|||
f2 t = h0 t *^ ( T p )
|
||||
f3 t = h3 t *^ ( T r )
|
||||
|
||||
loop :: forall s. Unboxed.MVector s Double -> Int -> ST s ( Cubic.Bezier ( ℝ 2 ), ArgMax Double Double )
|
||||
loop :: forall s. MutablePrimArray s Double -> Int -> ST s ( Cubic.Bezier ( ℝ 2 ), ArgMax Double Double )
|
||||
loop ts count = do
|
||||
let
|
||||
hermiteParameters :: Mat22 -> T ( ℝ 2 ) -> Int -> [ ℝ 2 ] -> ST s ( T ( ℝ 2 ) )
|
||||
hermiteParameters ( Mat22 a11 a12 _ a22 ) ( V2 b1 b2 ) i ( q : rest ) = do
|
||||
ti <- Unboxed.MVector.unsafeRead ts i
|
||||
ti <- readPrimArray ts i
|
||||
let
|
||||
f0i, f1i, f2i, f3i :: T ( ℝ 2 )
|
||||
f0i = f0 ti
|
||||
|
@ -254,7 +251,7 @@ fitPiece dist_tol t_tol maxIters p tp qs r tr =
|
|||
-- so that t_i' is a better approximation of the parameter
|
||||
-- at which the curve is closest to q_i.
|
||||
( dts_changed, argmax_sq_dist ) <- ( `execStateT` ( False, Max ( Arg 0 0 ) ) ) $ for_ ( zip qs [ 0 .. ] ) \( q, i ) -> do
|
||||
ti <- lift ( Unboxed.MVector.unsafeRead ts i )
|
||||
ti <- lift ( readPrimArray ts i )
|
||||
let
|
||||
laguerreStepResult :: Complex Double
|
||||
laguerreStepResult = runST do
|
||||
|
@ -277,7 +274,7 @@ fitPiece dist_tol t_tol maxIters p tp qs r tr =
|
|||
sq_dist :: Double
|
||||
sq_dist = quadrance @( T ( ℝ 2 ) ) q ( Cubic.bezier @( T ( ℝ 2 ) ) bez ti' )
|
||||
modify' ( second ( <> Max ( Arg sq_dist ti' ) ) )
|
||||
lift ( Unboxed.MVector.unsafeWrite ts i ti' )
|
||||
lift ( writePrimArray ts i ti' )
|
||||
|
||||
case argmax_sq_dist of
|
||||
Max ( Arg max_sq_dist _ )
|
|
@ -10,6 +10,8 @@ module Math.Bezier.Stroke
|
|||
, computeStrokeOutline, joinWithBrush
|
||||
, withTangent
|
||||
|
||||
, RootSolvingAlgorithm(..) -- TODO: move this?
|
||||
|
||||
-- * Brush stroking
|
||||
|
||||
, brushStroke, envelopeEquation
|
||||
|
@ -127,8 +129,6 @@ import Math.Orientation
|
|||
, between
|
||||
)
|
||||
import Math.Roots
|
||||
( solveQuadratic, newtonRaphson )
|
||||
|
||||
|
||||
import Debug.Utils
|
||||
|
||||
|
@ -237,7 +237,8 @@ computeStrokeOutline ::
|
|||
, Show ptData, Show brushParams
|
||||
|
||||
)
|
||||
=> FitParameters
|
||||
=> RootSolvingAlgorithm
|
||||
-> FitParameters
|
||||
-> ( ptData -> usedParams )
|
||||
-> ( usedParams -> brushParams ) -- ^ assumed to be linear and non-decreasing
|
||||
-> ( forall {t} k (i :: t)
|
||||
|
@ -253,7 +254,7 @@ computeStrokeOutline ::
|
|||
, Seq FitPoint
|
||||
, [ Cusp ]
|
||||
)
|
||||
computeStrokeOutline fitParams ptParams toBrushParams brushFn spline@( Spline { splineStart = spt0 } ) = case ssplineType @clo of
|
||||
computeStrokeOutline rootAlgo fitParams ptParams toBrushParams brushFn spline@( Spline { splineStart = spt0 } ) = case ssplineType @clo of
|
||||
-- Open brush path with at least one segment.
|
||||
-- Need to add caps at both ends of the path.
|
||||
SOpen
|
||||
|
@ -355,7 +356,7 @@ computeStrokeOutline fitParams ptParams toBrushParams brushFn spline@( Spline {
|
|||
where
|
||||
|
||||
outlineInfo :: ptData -> Curve Open crvData ptData -> OutlineInfo
|
||||
outlineInfo = inline ( outlineFunction ptParams toBrushParams brushFn )
|
||||
outlineInfo = inline ( outlineFunction rootAlgo ptParams toBrushParams brushFn )
|
||||
|
||||
outlineFns :: Seq OutlineInfo
|
||||
outlineFns = go spt0 ( openCurves $ splineCurves ( adjustSplineType @Open spline ) )
|
||||
|
@ -517,7 +518,8 @@ outlineFunction
|
|||
-- Debugging.
|
||||
, Show ptData, Show brushParams
|
||||
)
|
||||
=> ( ptData -> usedParams )
|
||||
=> RootSolvingAlgorithm
|
||||
-> ( ptData -> usedParams )
|
||||
-> ( usedParams -> brushParams ) -- ^ assumed to be linear and non-decreasing
|
||||
-> ( forall {t} k (i :: t)
|
||||
. DiffInterp k i brushParams
|
||||
|
@ -529,7 +531,7 @@ outlineFunction
|
|||
-> ptData
|
||||
-> Curve Open crvData ptData
|
||||
-> OutlineInfo
|
||||
outlineFunction ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
||||
outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
||||
let
|
||||
|
||||
usedParams :: C 2 ( ℝ 1 ) usedParams
|
||||
|
@ -566,7 +568,7 @@ outlineFunction ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
|||
|
||||
fwdBwd :: OutlineFn
|
||||
fwdBwd t
|
||||
= solveEnvelopeEquations t path_t path'_t ( fwdOffset, bwdOffset )
|
||||
= solveEnvelopeEquations rootAlgo t path_t path'_t ( fwdOffset, bwdOffset )
|
||||
( curves t )
|
||||
where
|
||||
|
||||
|
@ -953,15 +955,23 @@ splineCurveFns co spls
|
|||
Bezier3To { controlPoint1 = p1, controlPoint2 = p2, curveEnd = NextPoint p3 }
|
||||
-> bezier3 @k @i @( ℝ 2 ) co $ Cubic.Bezier p0 p1 p2 p3
|
||||
|
||||
-- | Which method to use to solve the envelope equation?
|
||||
data RootSolvingAlgorithm
|
||||
-- | Use the Newton–Raphson method.
|
||||
= NewtonRaphson { maxIters :: Word, precision :: Int }
|
||||
-- | Use the modified Halley M2 method.
|
||||
| HalleyM2 { maxIters :: Word, precision :: Int }
|
||||
|
||||
-- | Solve the envelope equations at a given point \( t = t_0 \), to find
|
||||
-- \( s_0 \) such that \( c(t_0, s_0) \) is on the envelope of the brush stroke.
|
||||
solveEnvelopeEquations :: ℝ 1 -- ^ @t@ (for debugging only)
|
||||
solveEnvelopeEquations :: RootSolvingAlgorithm
|
||||
-> ℝ 1 -- ^ @t@ (for debugging only)
|
||||
-> ℝ 2
|
||||
-> T ( ℝ 2 )
|
||||
-> ( Offset, Offset )
|
||||
-> Seq ( ℝ 1 -> StrokeDatum 2 () )
|
||||
-> ( ( ℝ 2, T ( ℝ 2 ) ), ( ℝ 2, T ( ℝ 2 ) ) )
|
||||
solveEnvelopeEquations _t path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
||||
solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
||||
= ( fwdSol, ( bwdPt, -1 *^ bwdTgt ) )
|
||||
|
||||
where
|
||||
|
@ -999,12 +1009,18 @@ solveEnvelopeEquations _t path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
|||
sol :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> Double -> ( Bool, ℝ 2, T ( ℝ 2 ) )
|
||||
sol f is0 =
|
||||
let ( good, is ) =
|
||||
case newtonRaphson maxIters precision domain ( eqn f ) is0 of
|
||||
case runSolveMethod ( eqn f ) is0 of
|
||||
Nothing -> ( False, is0 )
|
||||
Just is1 -> ( True , is1 )
|
||||
( ds, dcdt ) = finish f is
|
||||
in ( good, ds, dcdt )
|
||||
|
||||
runSolveMethod = case rootAlgo of
|
||||
HalleyM2 { maxIters, precision } ->
|
||||
halleyM2 maxIters precision
|
||||
NewtonRaphson { maxIters, precision } ->
|
||||
newtonRaphson maxIters precision domain
|
||||
|
||||
finish :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> Double -> ( ℝ 2, T ( ℝ 2 ) )
|
||||
finish f is =
|
||||
let (i, s) = fromDomain is in
|
||||
|
@ -1037,17 +1053,13 @@ solveEnvelopeEquations _t path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
|||
-- ] )
|
||||
( value @Double @2 @( ℝ 2 ) dstroke, dcdt )
|
||||
|
||||
eqn :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> ( Double -> ( Double, Double ) )
|
||||
eqn :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> ( Double -> (# Double, Double #) )
|
||||
eqn fs is =
|
||||
let (i, s) = fromDomain is
|
||||
in case ( fs `Seq.index` i ) ( ℝ1 s ) of
|
||||
StrokeDatum { ee = D12 ee _ ee_s } ->
|
||||
coerce ( ee, ee_s )
|
||||
coerce (# ee, ee_s #)
|
||||
|
||||
maxIters :: Word
|
||||
maxIters = 20
|
||||
precision :: Int
|
||||
precision = 8
|
||||
n :: Int
|
||||
n = Seq.length strokeData
|
||||
domain :: ( Double, Double )
|
|
@ -4,9 +4,6 @@
|
|||
|
||||
{-# OPTIONS_GHC -Wno-orphans #-}
|
||||
|
||||
{-# OPTIONS_GHC -ddump-splices -ddump-simpl -ddump-cmm -ddump-to-file -dno-typeable-binds
|
||||
-dsuppress-unfoldings -dsuppress-coercions #-}
|
||||
|
||||
module Math.Interval
|
||||
( 𝕀(𝕀), inf, sup
|
||||
, scaleInterval
|
||||
|
@ -32,7 +29,7 @@ import Data.Group
|
|||
import Data.Group.Generics
|
||||
( )
|
||||
|
||||
-- splines
|
||||
-- brush-strokes
|
||||
import Math.Algebra.Dual
|
||||
import Math.Interval.Internal
|
||||
( 𝕀(𝕀), inf, sup, scaleInterval )
|
|
@ -136,6 +136,7 @@ instance Transcendental ( 𝕀 Double ) where
|
|||
atan = withHW Prelude.atan
|
||||
|
||||
{-# INLINE withHW #-}
|
||||
-- | Internal function: use @rounded-hw@ to define a function on intervals.
|
||||
withHW :: (Interval.Interval a -> Interval.Interval b) -> 𝕀 a -> 𝕀 b
|
||||
withHW f = \ ( 𝕀 lo hi ) ->
|
||||
case f ( Interval.I ( Rounded lo ) ( Rounded hi ) ) of
|
|
@ -13,6 +13,9 @@ module Math.Roots
|
|||
|
||||
-- * Newton–Raphson
|
||||
, newtonRaphson
|
||||
|
||||
-- * Modified Halley's method M2
|
||||
, halleyStep, halleyM2
|
||||
)
|
||||
where
|
||||
|
||||
|
@ -43,10 +46,6 @@ import Data.Primitive.PrimArray
|
|||
import Data.Primitive.Types
|
||||
( Prim )
|
||||
|
||||
-- prim-instances
|
||||
import Data.Primitive.Instances
|
||||
() -- instance Prim a => Prim ( Complex a )
|
||||
|
||||
-- MetaBrush
|
||||
import Math.Epsilon
|
||||
( epsilon, nearZero )
|
||||
|
@ -299,15 +298,15 @@ derivative p = do
|
|||
-- https://github.com/boostorg/math/blob/0dc6a70caa6bbec2b6ae25eede36c430f0ccae13/include/boost/math/tools/roots.hpp#L217
|
||||
{-# SPECIALISE
|
||||
newtonRaphson
|
||||
:: Word -> Int -> ( Double, Double ) -> ( Double -> ( Double, Double ) ) -> Double -> Maybe Double
|
||||
:: Word -> Int -> ( Double, Double ) -> ( Double -> (# Double, Double #) ) -> Double -> Maybe Double
|
||||
#-}
|
||||
{-# INLINEABLE newtonRaphson #-}
|
||||
newtonRaphson :: ( RealFloat r, Show r )
|
||||
=> Word -- ^ maximum number of iterations
|
||||
-> Int -- ^ desired digits of precision
|
||||
-> ( r, r ) -- ^ @(min_x, max_x)@.
|
||||
-> ( r -> ( r, r ) ) -- ^ function and its derivative
|
||||
-> r -- ^ initial guess
|
||||
=> Word -- ^ maximum number of iterations
|
||||
-> Int -- ^ desired digits of precision
|
||||
-> ( r, r ) -- ^ @(min_x, max_x)@.
|
||||
-> ( r -> (# r, r #) ) -- ^ function and its derivative
|
||||
-> r -- ^ initial guess
|
||||
-> Maybe r
|
||||
newtonRaphson maxIters digits ( min_x, max_x ) f x0 =
|
||||
doNewtonRaphson f maxIters factor min_x max_x 0 0 0 x0 maxRealFloat maxRealFloat
|
||||
|
@ -315,7 +314,7 @@ newtonRaphson maxIters digits ( min_x, max_x ) f x0 =
|
|||
!factor = encodeFloat 1 ( 1 - digits )
|
||||
|
||||
doNewtonRaphson :: ( Fractional r, Ord r, Show r )
|
||||
=> ( r -> (r, r) )
|
||||
=> ( r -> (# r, r #) )
|
||||
-> Word
|
||||
-> r
|
||||
-> r -> r
|
||||
|
@ -329,7 +328,7 @@ doNewtonRaphson f maxIters factor min_x max_x min_f_x max_f_x f_x_prev x δ1 δ2
|
|||
where
|
||||
go min_x max_x min_f_x max_f_x f_x_prev !iters !x !δ1 !δ2 =
|
||||
case f x of
|
||||
( f_x, f'_x )
|
||||
(# f_x, f'_x #)
|
||||
| f_x == 0
|
||||
-> Just x
|
||||
| ( new_x, δ, δ1 ) <- newtonRaphsonStep f min_x max_x f_x_prev x f_x f'_x δ1 δ2
|
||||
|
@ -349,7 +348,7 @@ doNewtonRaphson f maxIters factor min_x max_x min_f_x max_f_x f_x_prev x δ1 δ2
|
|||
go min_x max_x min_f_x max_f_x f_x ( iters + 1 ) new_x δ δ1
|
||||
|
||||
newtonRaphsonStep :: ( Fractional r, Ord r, Show r )
|
||||
=> ( r -> ( r, r ) )
|
||||
=> ( r -> (# r, r #) )
|
||||
-> r
|
||||
-> r -> r -> r
|
||||
-> r -> r
|
||||
|
@ -380,7 +379,7 @@ newtonRaphsonStep f min_x max_x f_x_prev x f_x f'_x δ1 δ2
|
|||
|
||||
-- Handle \( f'(x_0) = 0 \).
|
||||
zeroDerivativeStep :: ( Fractional r, Ord r, Show r )
|
||||
=> ( r -> ( r, r ) )
|
||||
=> ( r -> (# r, r #) )
|
||||
-> r
|
||||
-> r -> r
|
||||
-> r
|
||||
|
@ -390,7 +389,7 @@ zeroDerivativeStep f min_x max_x f_x_prev x f_x δ
|
|||
-- Handle zero derivative on first iteration.
|
||||
| f_x_prev == 0
|
||||
, x_prev <- if x <= 0.5 * ( min_x + max_x ) then max_x else min_x
|
||||
, ( f_x_prev, _ ) <- f x_prev
|
||||
, (# f_x_prev, _ #) <- f x_prev
|
||||
, δ <- x_prev - x
|
||||
= finish f_x_prev δ
|
||||
| otherwise
|
||||
|
@ -430,3 +429,52 @@ maxDouble :: Double
|
|||
maxDouble = D# 1.7976931348623157e308##
|
||||
|
||||
-}
|
||||
|
||||
--------------------------------------------------------------------------------
|
||||
-- Halley's method (WIP).
|
||||
|
||||
-- | Take a single step with Halley's method.
|
||||
halleyStep :: Fractional a => (# a, a, a, a #) -> a
|
||||
halleyStep (# x, f, f', f'' #) =
|
||||
x - 2 * f * f' / ( 2 * f' ^ ( 2 :: Int ) - f * f'' )
|
||||
|
||||
-- | Take a single step in the M2 modified Halley method.
|
||||
--
|
||||
-- Taken from @Some variants of Halley’s method with memory and their applications for solving several chemical problems@
|
||||
-- by A. Cordero, H. Ramos & J.R. Torregrosa, J Math Chem 58, 751–774 (2020).
|
||||
--
|
||||
-- @https://doi.org/10.1007/s10910-020-01108-3@
|
||||
halleyM2Step :: Fractional a => (# a, (# a, a #) #) -> (# a, (# a, a #) #) -> a
|
||||
halleyM2Step (# x_nm1, (# f_nm1, f'_nm1 #) #) (# x_n, (# f_n, f'_n #) #) =
|
||||
num / denom
|
||||
where
|
||||
u = f_n * f_nm1 * (f_n - f_nm1)
|
||||
dx = x_n - x_nm1
|
||||
g1 = f_nm1 ^ ( 2 :: Int ) * f'_n
|
||||
g2 = f_n ^ ( 2 :: Int ) * f'_nm1
|
||||
num = (x_n + x_nm1) * u - dx * ( g1 * x_n + g2 * x_nm1)
|
||||
denom = 2 * u - dx * ( g1 + g2 )
|
||||
|
||||
{-# SPECIALISE
|
||||
halleyM2
|
||||
:: Word -> Int -> ( Double -> (# Double, Double #) ) -> Double -> Maybe Double
|
||||
#-}
|
||||
{-# INLINEABLE halleyM2 #-}
|
||||
halleyM2 :: ( RealFloat r, Show r )
|
||||
=> Word -- ^ maximum number of iterations
|
||||
-> Int -- ^ desired digits of precision
|
||||
-> ( r -> (# r, r #) ) -- ^ function and its derivative
|
||||
-> r -- ^ initial guess
|
||||
-> Maybe r
|
||||
halleyM2 maxIters digits f x0 =
|
||||
let y0 = (# x0, f x0 #)
|
||||
in go 0 y0 y0
|
||||
where
|
||||
!factor = encodeFloat 1 ( 1 - digits )
|
||||
go i y_nm1 y_n@(# x_n, _ #) =
|
||||
let x_np1 = halleyM2Step y_nm1 y_n
|
||||
in if | i >= maxIters
|
||||
|| abs ( x_np1 - x_n ) < abs ( x_n * factor )
|
||||
-> Just x_np1
|
||||
| otherwise
|
||||
-> go (i+1) y_n (# x_n, f x_np1 #)
|
|
@ -1,9 +1,12 @@
|
|||
packages: .
|
||||
packages: brush-strokes
|
||||
, .
|
||||
|
||||
constraints:
|
||||
acts -finitary,
|
||||
rounded-hw -pure-hs -c99 -avx512 +ghc-prim -x87-long-double
|
||||
|
||||
brush-strokes +use-fma,
|
||||
rounded-hw -pure-hs -c99 -avx512 +ghc-prim -x87-long-double,
|
||||
text -simdutf
|
||||
-- text +simdutf causes the "digit" package to fail to build with undefined symbol linker errors
|
||||
|
||||
-- Fix a severe bug in Waargonaut (no corresponding Hackage release???)
|
||||
source-repository-package
|
||||
|
@ -12,27 +15,23 @@ source-repository-package
|
|||
tag: 5f838582a8c5aae1a198ecd4958729e53a6b03cf
|
||||
|
||||
allow-newer:
|
||||
*:base, *:ghc, *:ghc-prim, *:template-haskell,
|
||||
*:text
|
||||
|
||||
-------------
|
||||
-- GHC 9.2 --
|
||||
-------------
|
||||
|
||||
allow-newer:
|
||||
*:base, *:template-haskell, *:ghc-prim,
|
||||
acts:deepseq,
|
||||
digit:lens,
|
||||
eigen:primitive,
|
||||
eigen:transformers,
|
||||
gi-cairo-connector:mtl,
|
||||
hedgehog:resourcet,
|
||||
JuicyPixels:zlib,
|
||||
natural:lens,
|
||||
records-sop:deepseq,
|
||||
waargonaut:bifunctors,
|
||||
waargonaut:lens,
|
||||
waargonaut:records-sop,
|
||||
waargonaut:semigroups, waargonaut:text,
|
||||
waargonaut:vector, waargonaut:witherable,
|
||||
|
||||
-- records-sop
|
||||
source-repository-package
|
||||
type: git
|
||||
location: https://github.com/kosmikus/records-sop
|
||||
tag: abab99b4b870fce55e81dd03d4e41fb50502ca4e
|
||||
waargonaut:semigroups,
|
||||
waargonaut:text,
|
||||
waargonaut:vector,
|
||||
waargonaut:witherable,
|
||||
|
||||
-------------
|
||||
-- GHC 9.4 --
|
||||
|
@ -44,13 +43,6 @@ source-repository-package
|
|||
location: https://github.com/chessai/eigen
|
||||
tag: 1790fdf9138970dde0dbabf8b270698145a4a88c
|
||||
|
||||
-- rounded-hw
|
||||
source-repository-package
|
||||
type: git
|
||||
location: https://github.com/minoki/haskell-floating-point
|
||||
subdir: rounded-hw
|
||||
tag: c141bc8435c556e94d51254479a8213698679261
|
||||
|
||||
-------------
|
||||
-- GHC 9.6 --
|
||||
-------------
|
||||
|
|
|
@ -78,7 +78,7 @@ import Math.Bezier.Cubic.Fit
|
|||
import Math.Bezier.Spline
|
||||
( Spline(..), Curves(..), Curve(..), NextPoint(..) )
|
||||
import Math.Bezier.Stroke
|
||||
( invalidateCache )
|
||||
( RootSolvingAlgorithm(..), invalidateCache )
|
||||
import Math.Linear
|
||||
( ℝ(..) )
|
||||
import MetaBrush.Action
|
||||
|
@ -200,15 +200,16 @@ runApplication application = do
|
|||
fileBarTabsTVar <- STM.newTVarIO @( Map Unique FileBarTab ) Map.empty
|
||||
showGuidesTVar <- STM.newTVarIO @Bool True
|
||||
maxHistorySizeTVar <- STM.newTVarIO @Int 1000
|
||||
fitParametersTVar <- STM.newTVarIO @FitParameters
|
||||
( FitParameters
|
||||
fitParametersTVar <- STM.newTVarIO @FitParameters $
|
||||
FitParameters
|
||||
{ maxSubdiv = 5 --2 --3 -- 6
|
||||
, nbSegments = 3 --3 --6 -- 12
|
||||
, dist_tol = 0.1 -- 5e-3
|
||||
, t_tol = 0.1 -- 1e-4
|
||||
, maxIters = 5 -- 100
|
||||
}
|
||||
)
|
||||
rootsAlgoTVar <- STM.newTVarIO @RootSolvingAlgorithm $
|
||||
HalleyM2 { maxIters = 20, precision = 8 }
|
||||
|
||||
-- Put all these stateful variables in a record for conciseness.
|
||||
let
|
||||
|
@ -321,33 +322,34 @@ runApplication application = do
|
|||
case needsRecomputation of
|
||||
False -> STM.retry
|
||||
True -> do
|
||||
mbDocNow <- fmap present <$> activeDocument variables
|
||||
case mbDocNow of
|
||||
Nothing -> pure ( pure . const $ blankRender colours )
|
||||
Just doc -> do
|
||||
modifiers <- STM.readTVar modifiersTVar
|
||||
mbMousePos <- STM.readTVar mousePosTVar
|
||||
mbHoldAction <- STM.readTVar mouseHoldTVar
|
||||
mbPartialPath <- STM.readTVar partialPathTVar
|
||||
mode <- STM.readTVar modeTVar
|
||||
showGuides <- STM.readTVar showGuidesTVar
|
||||
debug <- STM.readTVar debugTVar
|
||||
fitParameters <- STM.readTVar fitParametersTVar
|
||||
STM.writeTVar recomputeStrokesTVar False
|
||||
let
|
||||
addRulers :: ( ( Int32, Int32 ) -> Cairo.Render () ) -> ( ( Int32, Int32 ) -> Cairo.Render () )
|
||||
addRulers newRender viewportSize = do
|
||||
newRender viewportSize
|
||||
renderRuler
|
||||
colours viewportSize ViewportOrigin viewportSize
|
||||
mbMousePos mbHoldAction showGuides
|
||||
doc
|
||||
pure
|
||||
( addRulers <$> getDocumentRender
|
||||
colours fitParameters mode debug
|
||||
modifiers mbMousePos mbHoldAction mbPartialPath
|
||||
doc
|
||||
)
|
||||
mbDocNow <- fmap present <$> activeDocument variables
|
||||
case mbDocNow of
|
||||
Nothing -> pure ( pure . const $ blankRender colours )
|
||||
Just doc -> do
|
||||
modifiers <- STM.readTVar modifiersTVar
|
||||
mbMousePos <- STM.readTVar mousePosTVar
|
||||
mbHoldAction <- STM.readTVar mouseHoldTVar
|
||||
mbPartialPath <- STM.readTVar partialPathTVar
|
||||
mode <- STM.readTVar modeTVar
|
||||
showGuides <- STM.readTVar showGuidesTVar
|
||||
debug <- STM.readTVar debugTVar
|
||||
fitParameters <- STM.readTVar fitParametersTVar
|
||||
rootsAlgo <- STM.readTVar rootsAlgoTVar
|
||||
STM.writeTVar recomputeStrokesTVar False
|
||||
let
|
||||
addRulers :: ( ( Int32, Int32 ) -> Cairo.Render () ) -> ( ( Int32, Int32 ) -> Cairo.Render () )
|
||||
addRulers newRender viewportSize = do
|
||||
newRender viewportSize
|
||||
renderRuler
|
||||
colours viewportSize ViewportOrigin viewportSize
|
||||
mbMousePos mbHoldAction showGuides
|
||||
doc
|
||||
pure
|
||||
( addRulers <$> getDocumentRender
|
||||
colours rootsAlgo fitParameters mode debug
|
||||
modifiers mbMousePos mbHoldAction mbPartialPath
|
||||
doc
|
||||
)
|
||||
renderDoc <- stToIO getRenderDoc
|
||||
STM.atomically do
|
||||
STM.writeTVar documentRenderTVar renderDoc
|
||||
|
|
|
@ -41,6 +41,8 @@ import Data.HashMap.Strict
|
|||
-- MetaBrush
|
||||
import Math.Bezier.Cubic.Fit
|
||||
( FitParameters )
|
||||
import Math.Bezier.Stroke
|
||||
( RootSolvingAlgorithm )
|
||||
import Math.Linear
|
||||
( ℝ(..) )
|
||||
import {-# SOURCE #-} MetaBrush.Action
|
||||
|
@ -99,6 +101,7 @@ data Variables
|
|||
, showGuidesTVar :: !( STM.TVar Bool )
|
||||
, maxHistorySizeTVar :: !( STM.TVar Int )
|
||||
, fitParametersTVar :: !( STM.TVar FitParameters )
|
||||
, rootsAlgoTVar :: !( STM.TVar RootSolvingAlgorithm )
|
||||
}
|
||||
|
||||
--------------------------------------------------------------------------------
|
||||
|
|
|
@ -74,6 +74,7 @@ import Math.Bezier.Spline
|
|||
import Math.Bezier.Stroke
|
||||
( Cusp(..), CachedStroke(..), invalidateCache
|
||||
, computeStrokeOutline
|
||||
, RootSolvingAlgorithm
|
||||
)
|
||||
import Math.Linear
|
||||
( ℝ(..), T(..) )
|
||||
|
@ -147,12 +148,12 @@ blankRender :: Colours -> Cairo.Render ()
|
|||
blankRender _ = pure ()
|
||||
|
||||
getDocumentRender
|
||||
:: Colours -> FitParameters -> Mode -> Bool
|
||||
:: Colours -> RootSolvingAlgorithm -> FitParameters -> Mode -> Bool
|
||||
-> Set Modifier -> Maybe ( ℝ 2 ) -> Maybe HoldAction -> Maybe PartialPath
|
||||
-> Document
|
||||
-> ST RealWorld ( ( Int32, Int32 ) -> Cairo.Render () )
|
||||
getDocumentRender
|
||||
cols fitParams mode debug
|
||||
cols rootAlgo fitParams mode debug
|
||||
modifiers mbMousePos mbHoldEvent mbPartialPath
|
||||
doc@( Document { viewportCenter = ℝ2 cx cy, zoomFactor, documentContent = content } )
|
||||
= do
|
||||
|
@ -214,7 +215,7 @@ getDocumentRender
|
|||
-> previewStroke :<| foldMap visibleStrokes ( strokes content )
|
||||
_ -> foldMap visibleStrokes ( strokes content )
|
||||
|
||||
strokesRenderData <- traverseMaybe ( sequenceA . strokeRenderData fitParams ) modifiedStrokes
|
||||
strokesRenderData <- traverseMaybe ( sequenceA . strokeRenderData rootAlgo fitParams ) modifiedStrokes
|
||||
|
||||
let
|
||||
renderSelectionRect :: Cairo.Render ()
|
||||
|
@ -275,8 +276,8 @@ instance NFData StrokeRenderData where
|
|||
-- - the computed outline (using fitting algorithm),
|
||||
-- - the brush shape function.
|
||||
-- - Otherwise, this consists of the underlying spline path only.
|
||||
strokeRenderData :: FitParameters -> Stroke -> Maybe ( ST RealWorld StrokeRenderData )
|
||||
strokeRenderData fitParams
|
||||
strokeRenderData :: RootSolvingAlgorithm -> FitParameters -> Stroke -> Maybe ( ST RealWorld StrokeRenderData )
|
||||
strokeRenderData rootAlgo fitParams
|
||||
( Stroke
|
||||
{ strokeSpline = spline :: StrokeSpline clo ( Record pointFields )
|
||||
, strokeBrush = ( strokeBrush :: Maybe ( Brush brushFields ) )
|
||||
|
@ -301,7 +302,7 @@ strokeRenderData fitParams
|
|||
|
||||
-- Compute the outline using the brush function.
|
||||
( outline, fitPts, cusps ) <-
|
||||
computeStrokeOutline @clo fitParams
|
||||
computeStrokeOutline @clo rootAlgo fitParams
|
||||
( toUsedParams . brushParams ) embedUsedParams brushFn
|
||||
spline
|
||||
pure $
|
||||
|
|
|
@ -179,14 +179,15 @@ updateInfoBar viewportDrawingArea ( InfoBar {..} ) ( Variables { mousePosTVar }
|
|||
GTK.labelSetText botRightPosText $ Text.pack ( "x: " <> fixed 6 2 r <> "\ny: " <> fixed 6 2 b )
|
||||
|
||||
fixed :: Int -> Int -> Double -> String
|
||||
fixed digitsBefore digitsAfter x = case second tail . break ( == '.' ) $ showFFloat ( Just digitsAfter ) x "" of
|
||||
( as, bs ) ->
|
||||
let
|
||||
l, r :: Int
|
||||
l = length as
|
||||
r = length bs
|
||||
in
|
||||
replicate ( digitsBefore - l ) ' ' <> as <> "." <> bs <> replicate ( digitsAfter - r ) '0'
|
||||
fixed digitsBefore digitsAfter x =
|
||||
case second (drop 1) . break ( == '.' ) $ showFFloat ( Just digitsAfter ) x "" of
|
||||
( as, bs ) ->
|
||||
let
|
||||
l, r :: Int
|
||||
l = length as
|
||||
r = length bs
|
||||
in
|
||||
replicate ( digitsBefore - l ) ' ' <> as <> "." <> bs <> replicate ( digitsAfter - r ) '0'
|
||||
|
||||
na :: IsString a => a
|
||||
na = " n/a"
|
||||
|
|
|
@ -34,7 +34,7 @@ import qualified Linear.V2 as Linear
|
|||
import Control.Monad.Trans.Reader
|
||||
( runReaderT )
|
||||
|
||||
-- splines
|
||||
-- brush-strokes
|
||||
import Math.Bezier.Spline
|
||||
( Spline, SplineType(..) )
|
||||
import Math.Bezier.Stroke
|
||||
|
|
|
@ -56,7 +56,7 @@ import qualified Text.Parsec.Error as Parsec
|
|||
import Data.Text
|
||||
( Text )
|
||||
|
||||
-- splines
|
||||
-- brush-strokes
|
||||
import Math.Bezier.Spline
|
||||
( Spline(..), SplineType(..), KnownSplineType
|
||||
, Curves(..), Curve(..), NextPoint(..)
|
||||
|
|
Loading…
Reference in a new issue